I think it's something about your operating system, not InDesign. Here I'm using my copy of InDesign, using the same version of Mac OS X 10.8.4 as you, and the Search feature in the Open dialog works fine:

But, just to be sure, try restoring InDesign preferences to see if that might be interfering. Here's how:

I thought of something else. Open up another program like Microsoft Word and try a search there in the Open dialog. If it works, it could be InDesign conflicting. If it's doesn't, it's something in your system.

You probably know that, but keep an eye at the labels that determine the scope of the search. In Peter's screenshot, in the top left corner, below the "Lalita" disk, you see a line containing "Search:", "This Mac", and "Desktop". The "This Mac" label is selected, so the search is being performed in the whole system. If Peter had chosen "Desktop", only his desktop and the folders inside it would have been searched. Maybe your searches are returning nothing because you're searching only the document's current folder instead of the whole disk or your home directory.

Another possibility is that your Mac is not indexing the files. Open System Preferences -> Spotlight and take a look at the "Search Results" tab; maybe "Documents" is disabled. Also check the "Privacy" tab: if you include a disk or directory in the list, none of its contents will be indexed by the system, which prevents them to appear in search queries.

I have contacted Adobe and they had me run software update and update my InDesign to 8.0.2, relaunched InDesign to do a search: didn't work. Then we created a new USER and tried to do a search with InDesign there: It worked. So then we went back to my account an opened Indesign and deleted InDesign Permissions: didn't work. So they deemed that it was OSX permissions. I have run disk utility and repaired what came up: Still didn't work.